Question
Asked Aug 26, 2019
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13.1-4. Temperature Distribution in a Hollow Sphere. Derive Eq. (13.1-18) for the steady-
state conduction of heat in a hollow sphere. Also, derive an equation that shows that
the temperature varies hyperbolically with the radius
T- T
Ans.
sqty
Juo e
12
T, T
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13.1-4. Temperature Distribution in a Hollow Sphere. Derive Eq. (13.1-18) for the steady- state conduction of heat in a hollow sphere. Also, derive an equation that shows that the temperature varies hyperbolically with the radius T- T Ans. sqty Juo e 12 T, T

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Step 1

Consider a hollow sphere of constant density and thermal conductivity.

Let the outer surface is at temperature T2 and the inner surface is at temperature T1.

 

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(Heat flows radially outwards, Hollow sphere Element T2

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Step 2

Consider heat transfer in all direction with internal heat generation the general heat equation for sphere is given as

 

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1 + 1 K kr Ksin 0 rsin 0 a0 (1) +mpC P

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Step 3

When heat transfer occurs only in radial directions then,

When steady state hea...

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от от = 0 оф о0 от а Я, 30

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